An asymptotically sharp form of Ball's integral inequality

Abstract

We solve the open problem of determining the second order term in the asymptotic expansion of the integral in Ball's integral inequality. In fact, we provide a method by which one can compute any term in the expansion.

We also indicate how to derive an asymptotically sharp form of a generalized Ball's integral inequality.

Keywords

• Ball's integral inequality
• asymptotic expansion
• Bessel function
• Sinc function